What are the best possible methods and available software to compute the spin-state energetics of transition metal complexes?
For computing the spin-state in a metal complex there are many methods available. I'll focus in DFT as one of the most used methodologies.
In a single atom cluster (sometimes described as mononuclear complexes), DFT offers good results compared with wave-function multideterminantal methods.
On the other hand, if the complex is formed by two or more metallic centers, DFT has real troubles while finding the energy of antiferromagnetically coupled states. One of the most used approximations about this is the 'broken-symmetry' approach which permits to calculate the single determinant energy of a certain state. Nice reviews on this about metallic complexes are by Ruiz et. al..[1, 2] With this approach it is possible to somehow approximate the value of the magnetic exchange coupling that finally determines the relative energies of the different spin states, but one should be really careful concerning which particular expression is using for it.
- Ruiz, E.; Cano, J.; Alvarez, S.; Alemany, P. Broken symmetry approach to calculation of exchange coupling constants for homobinuclear and heterobinuclear transition metal complexes. J. Comput. Chem. 1999, 20 (13), 1391–1400. DOI: 10.1002/(SICI)1096-987X(199910)20:13%3C1391::AID-JCC6%3E3.0.CO;2-J.
- Ruiz, E.; Rodríguez-Fortea, A.; Cano, J.; Alvarez, S.; Alemany, P. About the calculation of exchange coupling constants in polynuclear transition metal complexes. J. Comput. Chem. 2003, 24 (8), 982–989. DOI: 10.1002/jcc.10257.
There's probably no answer to this question.
Best possible method? In general, just build up reasonable structures (don't tunnel vision into one), find their local minima on the given spin-states and just compare their energetics.
The best level of theory is also not really defined. One might say DFT, but I personally do not really trust DFT in general for problems like these. CCSD(T) could be performed, depending on your computational resources (remember, you need to optimize too, which you can probably do on MP2 level in this case and hope for the best), but don't be fooled into thinking CCSD(T) is the golden standard method. It is only the golden standard for large enough basis sets, which could also be an issue with transition metal complexes. Also for heavier elements, you might need to add spin-orbit corrections. Even worse: if the spin states (or just normal electronic states) are not separate enough, you really need a multireference method. Then we should be talking about MRCI, which is extremely complicated, and again, no general answer on how to do it.
As to what code to use, you have a plethora to choose from. Apart from the big names like Gaussian or Q-Chem, you might look into FHI-AIMS for the numerical basis set efficiency - however, this code really only is for DFT, which I would not suggest here. ORCA seems to do excellent on problems on this, and it also has a DMRG method built in, so I strongly suggest ORCA here. Molpro can also be considered for the extremely reliable spin-orbit coupling methods available. But for a general CCSD(T) calculation, I'd stick with the good old Gaussian, as that is, in my experience, the most reliable.